Complexity in Remote Sensing:A Literature Review, Synthesis and Position Paper

Robin WilsonID: 21985588

June 2, 2011

Contents

1 Introduction 2

2 Motivation 2

3 Is the remote sensing system a complex system? 33.1 What is the remote sensing system? . . . . . . . . . . . . . . . . . . . . . . 33.2 Is the remote sensing system complex? . . . . . . . . . . . . . . . . . . . . 3

3.2.1 Complex interactions between processes . . . . . . . . . . . . . . . 43.2.2 Boundaries between complex systems . . . . . . . . . . . . . . . . . 53.2.3 Chaos in image processing . . . . . . . . . . . . . . . . . . . . . . . 63.2.4 Intentional complexity . . . . . . . . . . . . . . . . . . . . . . . . . 7

3.3 Types of complexity in remote sensing . . . . . . . . . . . . . . . . . . . . 7

4 Case studies of complexity in the remote sensing system 84.1 Flow of complexity through image analysis procedures . . . . . . . . . . . 84.2 Complexity in Object-Based Image Analysis . . . . . . . . . . . . . . . . . 12

5 Opportunities for complex systems simulation in remote sensing 145.1 End-to-end simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155.2 Investigation of ‘pre-packaged’ algorithms . . . . . . . . . . . . . . . . . . . 155.3 Development of algorithms based on simulation . . . . . . . . . . . . . . . 16

6 Conclusion 17

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1 Introduction

In general, remote sensing is the act of obtaining information about an object from adistance. This can be applied in a number of situations, but in this paper I will focus onthe field of remote sensing and Earth observation which is primarily concerned with theobservation of the Earth’s surface from a distance (usually by satellites or aircraft) withthe aim of obtaining information about the surface of the Earth. Further to this, I willfocus on passive remote sensing in the optical domain, that is, remote sensing which usesthe sun as the source of the radiation (rather than creating any radiation from an artificialtransmitter) and operates in the optical wavelengths (approximately 0.4–1.4µm).

Remote sensing and Earth observation is a growing field and has expanded significantlyin recent years. There are now hundreds of Earth observation satellites in orbit aroundthe Earth providing many petabytes of data a year, and data derived from remote sensingsensors are used in applications from precision farming (D’Urso et al., 2010) and climatemodelling (Liang, 2007) to census data reconstruction (Watmough, 2010) and disastermanagement (Tralli et al., 2005). A number of authors are now stating that “Remotesensing has come of age” (Mather, 2010; Tang et al., 2009), but this has led to remotesensing data products being used with little thought to the process by which they wereacquired and the inherent errors and uncertainties in the data.

Complex systems science is a relatively new area of scientific research which focusses onunderstanding systems which have many interactions which are difficult to model math-ematically. I feel that complexity science is able to contribute significantly to the under-standing of remote sensing systems and the complex interactions which occur within them.In this paper I will endeavour to establish what the remote sensing system is, show that itis a complex (as opposed to just a complicated) system, and examine some of the ways inwhich this complexity manifests itself. Finally, I will examine the applicability of complexsystems simulation techniques to remote sensing problems.

2 Motivation

Remote sensing has developed significantly as a field since the first dedicated earth obser-vation satellites were launched in the early 1970s and is now used operationally for a widerange of purposes. With this apparent success in the field, it may be difficult to appreciatewhat remote sensing may stand to gain from a complex-systems based approach. However,remote sensing data products are not perfect, and the procedures that are used to producethem often do not work as well as we would hope. Despite the best efforts of researchersin the field, simple ‘point-and-click’ methods of pre-processing and analysis do not tend toprovide high quality results. In this paper I will argue that these problems are due to thecomplexity of the remote sensing system, and that applying a complex systems approachmay help to provide some solutions.

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Figure 1 – The major stages in the remote sensing process, which can be thought of as thecomponents of the remote sensing system

3 Is the remote sensing system a complex system?

3.1 What is the remote sensing system?

The image chain approach to remote sensing Schott (2007) splits the process of remotesensing into a number of individual steps which are joined to produce a chain leadingfrom acquisition of the image to the final output of information to the user. This chainis a processing system which I will refer to as the remote sensing system, and each of theprocessing systems is a component of this system.

At its simplest level, this system consists of three major stages: the acquisition of the data(usually in the form of images), the processing of this data, and then the display of theoutput to the user. These steps can then be broken down into substeps which are presentin almost all remote sensing projects, as shown in Figure 1. The pre-processing steps areparticularly important, as they alter the image data in an attempt to make it better reflectthe ‘reality’ of the situation on the ground (for example, by removing the effects of theatmosphere and the geometry of the sensor’s view of the Earth). Figure 2 shows an outlineof the stages involved in creating the GlobCover global land-cover map (Defourny et al.,2006) from a set of satellite images as an example of a multi-stage remote sensing system .

3.2 Is the remote sensing system complex?

There are a number of arguments for the remote sensing system being a complex system, asopposed to simply a complicated system (Amaral and Ottino, 2004), all of which approachthe question from a different point of view.

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Figure 2 – The outline procedure used to create the GlobCover global land-cover map(Defourny et al., 2006)

3.2.1 Complex interactions between processes

The image chain approach (Schott, 2007) emphasises the linkages between different pro-cedures carried out as part of the remote sensing process, but these linkages are describedas being simply between adjacent processes. I would argue that there are, in fact, manymore linkages than this, but that it is difficult to work out where these extra linkages are.

It should be remembered, of course, that Figure 1 is very simplified, and that each of thecomponents in that diagram is likely to have many sub-components which may interact in anon-linear manner. For example, the atmospheric correction component is likely to consistof a number of processes such as those listed below (used in the ATCOR atmosphericcorrection software; Richter, 2007)

• Selection of haze, cloud, water and clear pixels

• Haze removal

• Shadow removal

• Calculation of optical thickness

• Correction of path radiance

• Water vapour retrieval

• Reflectance spectrum calculation

• BRDF correction

Within each of these steps there is a complex model which is unlikely to be driven by asimple set of linear equations. For example, the selection of haze pixels in the algorithmabove is likely to be a complex system in itself possibly including a small simulation

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Table 1 – Major assumptions held in remote sensing studies, from Duggin and Robinove(1990)

1. Correlation between image and ground attributes is 1.002. Sensor radiometric calibration is known for each pixel3. Atmospheric affects do not affect the correlation or atmospheric effects have been perfectly

corrected for4. Sensor spatial response characteristics are accurately known and accounted for5. Sensor spectral response are accurately known at the time of image acquisition6. Image acquisition conditions were optimum with high radiometric contrast7. Image resolution is appropriate to detect and quantify features of interest8. Correlation between image and ground attributes is constant across the image9. Analytical procedures are appropriate and adequate to the task10. Imagery is analysed at an appropriate scale11. There is a means of verifying the accuracy of the quantification of ground attributes and

this process has been performed across the image

model within it. The rules connecting these components of the atmospheric correctionprocess change over the running time of the model, based on the parameters chosen andthe results of the previous stages. Furthermore, the order in which processes are carriedout will affect the results - leading to the question of whether, for example, performinggeometric correction before atmospheric correction is the ‘correct’ order, or whether theyshould be done the opposite way around.

It is important to note here that the linkages between these processes are not necessar-ily explicit linkages where code in later procedures explicitly references values calculatedpreviously. Instead, the linkages are often more subtle - involving the complex effects ofresults calculated earlier affecting the results at each subsequent stage.

These linkages can be partially explained as a complex uncertainty propagation processwhere major assumptions in each step of the process are not fully met, and these errors anduncertainties interact with each other. Duggin and Robinove (1990) examined a numberof the major assumptions made in remote sensing studies, most of which are never entirelytrue, (listed in Table 1). As more of these assumptions are invalidated, the chain ofinteractions leading from radiation source to final output product becomes more complex.

3.2.2 Boundaries between complex systems

The remote sensing system is an observing system, and therefore by its nature it is atthe boundary of a number of systems. In the case of an Earth observation system theseboundary systems are the Earth surface itself (including the processes driving spatial andtemporal change on it), the atmosphere through which the Earth is observed, and thehuman eye-brain system which is interpreting the image and/or map outputs. There is

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little disagreement that all of these systems are complex systems, and therefore the remotesensing system is at the boundary of three significantly complex systems.

This does not mean, of course, that the remote sensing system itself is complex, but it doessuggest that:

• When the remote sensing system is considered along with at least one of its bound-ary systems (for example, the atmosphere) then the resulting system is definitely acomplex system.

• The inputs to the remote sensing system will be from complex systems (the Earth andthe atmosphere) and therefore ‘stray complexity’ can leak into the remote sensingsystem. For example, all input data is filtered through the atmosphere, but wedon’t fully understand the complexity of the atmosphere, so this input data hasbeen modified in ways that we do not understand. This then leads to more complexinterations (as detailed above), between the remote sensing system itself and itsboundary systems.

3.2.3 Chaos in image processing

Many image processing algorithms are very sensitive to the initial image values provided tothem. For example, a very small change in the value of one pixel in the input can lead to alarge change in the output of a procedure such as unsupervised image classification. Thiscan be a problem as image values are inherently uncertain, both because of the method ofacquisition of the images and the pre-processing functions applied to the image.

Regardless of the quality of the sensor, the raw digital number (DN) recorded by thesensor is unlikely to be an accurate representation of the light reflected from the pixel inview. This is due to effects from the sensor itself (such as the point spread function, whichdescribes how much of the light entering the sensor actually originates from outside of thepixel) and from atmospheric effects (which, for example, cause scattering of light into thesensor’s aperture). Many procedures have been developed to try and correct these effectsby changing the DN values. However, as these effects are very difficult to correct (partlybecause the processes causing the effects are, themselves, complex and chaotic), so the finalDN values used as input to the main processing procedures could have significant errors.

It can easily be seen that small changes to the input DNs for a processing procedure (wellwithin the boundaries of the error discussed above) can lead to very large changes in theoutputs. This satisfies the common definition of chaos, where, in the words of Lorenz (in2006, aged 89) “the present determines the future, but the approximate present does notapproximately determine the future”, with the present and future referring, in this case,to the input and output of a processing algorithm.

Chaos can also be caused not by image data as such, but by choices made in algorithmdesign. For example, decision tree classifiers use a hierarchy of rules to classify the image.

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These rules are applied in a sequential manner, and therefore if the wrong decision is takenat the first rule, the end result could be erroneous - in complex systems terminology, thefirst decision is a tipping point. A wrong decision here could be caused by inaccurate imagedata (as above), or by bad choices for the conditions used for the rule. Regardless of thecause, a small inaccuracy in a choice made at the start of the processing has led to a largediscrepancy at the end - an example of chaos

3.2.4 Intentional complexity

So far, complexity in remote sensing has been discussed in terms of a ‘problem’ thatwe want to solve, with the aim of creating better outputs from remote sensing analyses.However, complexity can be useful, and a number of remote sensing procedures depend oncomplex interactions to work. Many classification techniques are forms of machine learningor artificial intelligence, and these are therefore trying to mirror the workings of the humanbrain - which is a complex system. Therefore, these techniques use techniques based oncomplex systems including the concept of self-organisation, which is a key feature of manycomplex systems.

For example, one of the most common unsupervised classification techniques is ISODATA,the Iterative Self-Organizing Data Analysis Technique. As its name suggests, this techniqueinvolves self-organisation of data, that is, the evolution of a system towards a state oforganisation, without any central authority imposing this organisation upon it. In the caseof ISODATA, the data will end up organised into a number of classes within which the datais fairly similar. This self-organisation is key to the utility of the algorithm, and thereforethe complexity underlying the formation of this organisation is very useful.

Similarly, neural networks such as the Multi-Layered Perceptron and Radial-Basis Func-tions have many applications within remote sensing (Mas and Flores, 2008), and theseare based on evolving a network of complex linkages between neurons (during the trainingphase) such that the network can then be used for classification. This evolution is designedto mirror the evolution and reinforcement of linkages between neurons found in the humanbrain, and has been very successful in producing high classification accuracies.

3.3 Types of complexity in remote sensing

In the literature on complex systems a difference has been recognised between naturalcomplexity and engineered complexity, with the latter being complexity that arises in sys-tems that have been explicitly designed by humans (whether in the traditional engineeringsense or not). Figure 3 gives examples of areas of remote sensing covered by both of thesecategories of complex systems, splitting engineered complex systems into those in whichthe complexity is intentional and those in which it is unintentional. This distinction isimportant, as in remote sensing we are often struggling to remove complexity which has

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Figure 3 – The different types of complexity found within remote sensing, with examples ofareas where they are found

unintentionally crept in to our systems and processes, but sometimes we are using thecomplexity in a system to do a useful job.

4 Case studies of complexity in the remote sensing

system

4.1 Flow of complexity through image analysis procedures

Wilson and Milton (2010) developed a technique for automatically extracting suitableatmospheric calibration sites from satellite images. Their study is used here as an exampleof a simple analysis procedure which still has to deal with complexity issues, particularlycomplexity flow through the process.

A flow chart showing an overview of the procedure carried out by Wilson and Milton (2010)is shown in Figure 4. However, this flowchart does not show the details of the issues whichmay affect this procedure. Figure 5 shows the details of the site selection procedure whichran within eCognition (an Object-based Image Analysis program). These classificationtests all depend on the data being correct, in terms of values and location, but this maynot be the case. The assumptions listed in Table 1 are unlikely to be true in this study,and this will significantly affect the quality of the output.

I will take one example of an assumption which may not hold true for the image data usedin this project, and show how the complex interactions based on this pass throughout theprocess. The images used were from the IKONOS satellite, which acquires images with a

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Figure 4 – Flow chart showing the procedures carried out by Wilson and Milton (2010)

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Figure 5 – Rules used for classification within eCognition

resolution of 4 metres from a 681km altitude. This is a high resolution to obtain from sucha height, and therefore there are likely to be significant inaccuracies in terms of the areaon the ground which contributes to the data stored in each pixel.

A method of quantifying this inaccuracy is known as the Point Spread Function (PSF),which describes which areas of the ground contribute to the radiance received at the sensorfor each pixel. Nearly all sensors have a PSF such that some of the received radiance comesfrom outside of the specified Ground Resolution Element (GRE; the defined pixel-size onthe ground), but this can vary between sensors. Table 2 shows the PSF for the SPOTsensor, and it can be seen that only 65% of the radiance received at the sensor, andtherefore stored in the pixel corresponding to the GRE under observation, actually camefrom that GRE.

This obviously has implications for the analysis of the image. The uncertainties and in-accuracies in the data will, in some unknown way, affect the result of the various analysisprocedures applied to the image. This is a form of complex interaction, as the uncertaintiesand inaccuracies of the original image data (caused by the optical sub-system) are affectingthe analysis sub-system in a non-linear and unpredictable manner.

Referring to the list of assumptions in Table 1, the sensor spatial characteristics are def-initely not accounted for, and this then makes a number of other assumptions false - forexample, not knowing the sensor spatial response affects the ability to resolve fine detail

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Table 2 – Point Spread Function for the SPOT sensor, from Ruiz and Lopez (2002). Thecentral cell is the GRE under observation, and the value in each cell is the percentage of theradiance received at the sensor which is sourced from that cell.

0.09 0.16 2.36 0.16 0.090.16 0.31 4.48 0.31 0.162.36 4.48 65.1 4.48 2.360.16 0.31 4.48 0.31 0.160.09 0.16 2.36 0.16 0.09

in the image (assumption 7) and the correlation between image and ground attributes (as-sumption 1). The latter assumption is particularly troublesome as the relationship betweenimage and ground attributes is usually assessed from the data in the acquired images, andif this data is incorrect (because of any of the other assumptions) then the calculation ofthe relationship between image attributes and ground attributes will be flawed.

The aim of the project was to select suitable sites for atmospheric calibration. These sitesmust fulfil a number of criteria: they must be flat, spatially uniform and temporally sta-ble, amongst other requirements. Spatial uniformity is assessed using the Getis statistic(Bannari et al., 2005), which is calculated using a 3x3 window across the image. TheseGetis statistic values are then assessed within the segmented image objects in the image.Of course, if there is a wide PSF then the pixels representing uniform areas will be ‘con-taminated’ by radiance from outside of the uniform areas, thus negatively biasing the Getisvalues for these image objects. This is an example of the adjacency effect, where adjacentpixels affect the radiance from the pixels under study.

This adjacency effect will not only affect the Getis statistic, but also the extraction ofendmember abundances and any processing based on the spectral data. This, of course,includes the segmentation of the image before classification, which - as it may be based ona complex algorithm itself - may be significantly different due to the adjacency effects.

This may seem a simple uncertainty propagation problem, but the complex comes throughthe interactions of all of the procedures with the unknown errors which have occurredearlier. Unfortunately, this means that simple methods to deal with the adjacency effectsare unlikely to work. Wilson and Milton (2010) performed an additional investigation tosee if shrinking each image object by one pixel around its border before using it for analysisimproved the results. It was thought this may be the case as the pixels around the edge ofthe object are those most likely to be affected by adjacency effects from the surroundingpixels in different objects, but this correction did not improve the accuracy. This suggeststhat the problem is too complex for simple measures like this to improve results.

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4.2 Complexity in Object-Based Image Analysis

Object-based Image Analysis (OBIA) is a method of image analysis which involves breakingdown an image into a number of image objects, each of which can be analysed individually.This provides more contextual information to image analysis techniques by operating atthe level of sets of pixels rather than individual pixels.

The first stage of OBIA is image segmentation, where the image is divided into a numberof image objects. A number of image segmentation methods exist, and they all aim toproduce image objects that are representative of real-world objects. For example, in ahigh-resolution aerial photograph the segmentation may extract individual buildings asseparate objects, and similarly for individual fields and roads. However, it is important torealise that the objects created from image segmentation do not necessarily have a one-to-one relationship with objects in the real world. This is one of the major assumptionsof OBIA, and it is almost always incorrect. Figure 6 shows an IKONOS satellite imageand the associated image objects produced by the segmentation process. It can be seenthat the entire roof of the large building (a warehouse in an industrial estate) has not beenextracted as a single image object, but has been split into a number of separate objects.These objects seem to represent the different segments of a sloping roof (it may be thatthe building has a ‘sawtooth’ roof). In some situations we may want to extract separatesegments like this, but in many situations this would be a case of over-segmentation.

It is accepted that image objects do not always correspond to real-world objects on theground, but can there ever be a one-to-one relationship between these? The surface of theEarth is complex and boundaries are often hard to define. For example, the boundary ofa building is fairly easy to define (and is often a straight line), but where is the boundarybetween woodland and heathland? Or the boundary between a lake and a field? Surelythis depends on the definitions of woodland and heathland, or the level of the lake whenthe measurements were taken.

Furthermore, landscapes are fractal (Goodchild, 1980; Gao and Xia, 1996), for example, itis well-known that there can never be a truly accurate measurement of the length of theUK coastline, as the resolution of measurement determines the length which is obtained- anything from one to infinity (Mandelbrot, 1967). Surely, however, this fractal natureapplies not just to coastlines, but to any boundaries on the Earth system, leaving us witha situation where length of an object boundary can be infinite, and the location of theboundary is uncertain. How, then, can we expect extract meaningful objects from satelliteimages when we cannot even define their boundaries accurately on the ground?

The fractal nature of landscapes also creates an issue with levels of description, or, in moregeographical terminology: scale and resolution. One of the defining features of complexsystems is that they behave differently at different levels of description (Amaral and Ottino,2004). In the case of remote sensing, the concept of ‘behaviour’ can be equated with theresponse of the image data to analysis procedures, and the quality of the resulting output.

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(a) IKONOS image of an industrial es-tate near Manchester

(b) Segmented image showing imageobjects

Figure 6 – Example of over-segmentation

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There has been significant work within the remote sensing and geographical informationcommunities on the problems of scale in their research. The seminal paper by Strahler et al.(1986) defined two scene models : H-resolution and L-resolution, defined by the featuresunder investigation being larger than the sensor resolution and smaller than the sensorresolution respectively. They suggest that these different scene types require differenttypes of analysis, and are susceptible to different types of uncertainties and inaccuracies.Further to this, remote sensing has also played its part in the development of a science ofscale (Marceau and Hay, 1999), a new field with many applications to complex systemsresearch. Goodchild and Quattrochi (1997), writing from a remote sensing perspective,defines the three major research questions of this science of scale as:

• What is the role of scale in the detection of patterns and processes, and how doesthis affect modelling?

• How can we identify areas of invariance of scale and scale thresholds?

• How can we implement multiscale approaches for analysis and modelling?

There is no doubt that these questions are key in the understanding of complex systems,particularly when examining complex systems through the medium of simulation models.They are also important questions in understanding remote sensing analysis. For example,when using OBIA there are two separate scales: the scale of the original image and thescale of the segmented image objects. The choice of these scales has a large influence onthe patterns which can be observed, and therefore on the relationship between the imageattributes and the ground attributes that we are trying to infer (assumption 1 in Table1). A major cause of this is the Modifiable Areal Unit Problem (MAUP; Openshaw andTaylor, 1979) which occurs when data (in this case image data) is aggregated into a numberof different areas (in this case the image objects). Openshaw found that the choice of theseareas (which is often arbitrary) significantly affects the results of the aggregation.

The MAUP, amongst other problems such as the ecological fallacy, show that the choiceof scales do not just have an influence on the patterns observed but they control the datathat we have, and the methods by which we can try and observe patterns.

5 Opportunities for complex systems simulation in re-

mote sensing

In recent years there has been significant progress in using simulation modelling as a tool tounderstand complex systems. These simulation models can be split into two types (Murray,2003): exploratory models which use simulation to explore the fundamental processes at theheart of complex systems, and predictive models which seek to model systems as accuratelyas possible to produce quantitative predictions. There is a place for both of these types of

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models in understanding complex systems, and the opportunities given below will includeboth types of modelling.

5.1 End-to-end simulation

Figure 1 shows the major stages in the remote sensing system, and it would seem sen-sible to attempt simulations of various parts of this system with the ultimate goal ofproducing a full end-to-end model of the system. This is a very ambitious task, and soit would seem to sensible to limit this to a simulation of a simple configuration of thesystem (for example, one satellite image acquisition from a well-characterised sensor withassociated pre-processing followed by a simple classification task). This model would be ofthe exploratory variety, as it would be almost impossible (and probably not very useful) toproduce a fully predictive model of the whole system. The aim of the model would be toinvestigate the effect of changing the parameters of various components. For example, ifthe atmospheric correction was changed, or a deconvolution filter was applied to attemptto remove the effects of the Point Spread Function, then the model would allow us tounderstand how the output would change.

This model would give an insight into the complex linkages within the image chain, but,as described above, each component of the chain has its own internal chain of complexsubcomponents. Therefore detailed simulation models of individual components or closelylinked components of the chain could be performed. For example, scene models (whichwould simulate scenes on the ground which sensors may observe) could be coupled withsensor models (which would simulate how the sensor observes the scenes it can see) toinvestigate how the parameters of the sensor and types of scene affect the resulting imagedata. This would be particularly useful when characterising new or as-yet-unbuilt sensors,and could be used to determine the utility of these sensors for certain types of work. Thisprocess is currently being carried out for the SkyDome sensor which is currently underdevelopment at the University of Southampton (Choi and Milton, 2011).

5.2 Investigation of ‘pre-packaged’ algorithms

Many remote sensing analyses require the use of ‘pre-packaged’ algorithms, such as thoseused for atmospheric correction, segmentation and classification. The exact details of theimplementation of these algorithms is not always available, meaning that they cannot bestudied mathematically or simulated in detail. Instead, investigation can be performed bymodelling the parameter spaces of these algorithms. This involves running the algorithmsmany times using a number of different parameters and quantifying the results. Infer-ences can then be made about the effect that each parameter has on the output, and theinteractions between each parameter can be observed. This type of modelling can apply

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dynamical systems concepts to these algorithms, plotting parameter choices as phase spacediagrams and investigating the attractors of the phase-space of the algorithms.

5.3 Development of algorithms based on simulation

The alternative to investigating existing algorithms is to develop new algorithms based onsimulation techniques. For example, atmospheric correction algorithms are just predictivemodels which are designed to give an accurate output. The development of these algo-rithms is a form of applied complex systems simulation: simulating a complex system (theatmosphere) with the purpose of inverting the model and using it for a practical purpose.

Although atmospheric dynamics was one of the first areas in which complexity and chaoswere studied (Lorenz, 1963), many existing atmospheric correction models seem to ignoremuch of this complexity and use deterministic models based on solving standard atmo-spheric modelling equations. There appears to be a gap here which could be filled bysimple atmospheric models based on complex systems simulation techniques such as cellu-lar automata and agent-based modelling. These models would not necessarily provide theaccuracy required for operational use in atmospheric correction, but they should providea useful method by which the essential characteristics of such models can be explored.

Furthermore, current atmospheric correction models do not take into account temporalchanges in the atmosphere. This is becoming more important as time series of satelliteand airborne imagery are becoming more widely available, and atmospheric correction isneeding to be performed across the whole set of images. When dealing with airborneimagery, even if temporal data is not explicitly used, different parts of the image arelikely to have been collected at different times.This is because the aircraft normally fliesa number of ‘flightlines’ as in Figure 7. Depending on the length of the flightlines thetime of data acquisition for points 1 and 2 could be very different. As far as the author isaware, no atmospheric correction software takes into account the progression of atmosphericconditions over the time period of the acquisition of the set of flightlines.

Another area with many possibilities for complex systems simulation is the modelling ofthe atmosphere with clouds. Most atmospheric models only take into account high cirruscloud and its haze-like effect on the transmission of radiation, but, of course, there aremany other types of cloud which are present in imagery. One may argue that it is of no usefor atmospheric correction algorithms to deal with cloudy skies, as these images are oftendiscarded when choosing images to process, but there are a number of reasons why gainingan understanding of the effects of cloud on the properties of the atmosphere is important:

• Clouds cannot always be avoided: Although many studies discard images withhigh cloud cover and mask out clouds in other images, this is not always possible.For example, Watmough (2010) needed to use images of India during the monsoonseason when it is almost impossible to avoid images with high cloud covers.

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Figure 7 – Example of the flightlines that may be flown by an aircraft to collect aerial images

• Clouds affect the optical properties of the whole sky: Atmospheric correctionalgorithms use a number of parameters describing the optical properties of the sky,and one of these is the diffuse to global ratio. This measures the proportion of thebrightness of the sky which comes from the solar disk compared to the brightness fromthe rest of the sky. However, clouds significantly affect this ratio and most models ofthe distribution of sky brightness used to calculate this ratio (such as Hooper andBrunger, 1980) are only designed to work with clear skies.

This is an area in which modelling techniques such as cellular automata could be used.Cellular automata have already been used for creating animated clouds (Dobashi et al.,1998), so it seems natural to try and extend these models to be useful for scientific purposes.

6 Conclusion

Until now there has not been a systematic study of complexity in passive, optical remotesensing. It is intended that this report will be the start of a detailed investigation intothe linkages between complex systems science and remote sensing, and that this will leadto significant benefits to the field of remote sensing. This report has demonstrated thatthe remote sensing system is a complex system, and has provided some case studies ofcomplexity in the system. It is now down to future work to extend this approach andproduce results which will be useful to applied remote sensing projects.

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